Deployment Experiments

A deployment test model was made using the same materials and techniques as described in Section 2.1.7. This model had scalloped edges, with a loading parameter of σ= 1 and an aspect ratio of γ = 1. It was made with 25.4µm-thick Mylarr, had diagonal lengthsLA =LB = 1.00 m, and 26 strips. The ligaments had widths of 1.0 mm and lengths of 4.3 mm. The model was laser-cut as three separate pieces that were spliced together using Kaptonr _tape.

The deployment test apparatus shown in Figure 2.27 was used to test the deployment concept. The apparatus consisted of four independent linear actuators to provide the deployment forces FB, FB0, F_A, F_A0, four force sensors to measure these deployment forces, and a suspension system to

partially offload the mass of the membrane.

Each linear actuator consisted of a lead screw (with a pitch of 2.54 mm) coupled to a stepper motor that drives a carriage back and forth along a rail. Each stepper motor (1.8◦full step size) was driven by a microstepping driver (AllegroTM4988 driving the motor with 1/4 steps). A microcontroller (Arduino Leonardo based on an AtmelR _{ATmega32u4) synchronized the four motors, as well as}

providing logic, displacement data logging, and an interface to a laptop personal computer. One 1/4 step (corresponding to a motion of 0.003 175 mm) was taken every 500µs. Slight microcontroller delays led to a carriage speed of 5.93 mm s−1. The motion of each carriage was controlled in open- loop based on the number of steps commanded.

A six-axis force sensor (ATI Industrial Automation Nano17) was mounted on each carriage, to measure the components of the deployment force with a resolution of 3.1µN. Moment components were also measured by the sensor, but these measurements were not used.

Note that the model was not packaged as tightly as in the packaging tests. That is, it was packaged with a larger minimum radius of curvature Rmin than dictated by Equation (2.18) and with gaps between layers. This is because the wrapping guides could not be included in this test; they would have to be removed before the unfolding stage, thus introducing mechanical complexity to the experiment. It is possible that a tightly packaged structure will deploy differently than a loosely packaged structure. The effect of packaging tightness on the deployment behavior warrants further experimentation.

Figure 2.28 shows the cage, with inner diameter of 37 mm and height of 49 mm, and the clip that were used for the deployment tests. The cage consisted of two laser-cut acrylic base plates, two 127µm-thick polyimide plates elastically bent into semicylinders by means of threaded rods that also attached the semicylinders to the base plates. The cage was constructed in two halves, which separate during the unfolding stage of the deployment. The inner faces of the semicylinders were coated with a spray-on PTFE-based dry lubricant (Saint-Gobain FluoroglideR_{) to reduce friction}

between the cage and the membrane during unwrapping. The location of the edge of the cage in relation to its center was measured to bexc= 19.6 mm, yc= 4.0 mm.

Figure 2.28: Membrane model, wrapped and inserted into the cage. The cage had a diameter of 37 mm and a height of 49 mm.

The clip was made using two paintbrush heads (7 mm × 4 mm cross section, 11 mm length) connected by a steel rod. The paintbrush bristles were pushed into the wrapped membrane stack, introducing a small spacing between the membrane strips. This ensured that the membrane strips would deploy one by one.

The membrane was deployed horizontally, minimizing the effects of gravity by suspending the clip about 0.25 m above the base of the two-axis deployment rig. Since the clip holds the middle of the membrane during most of the deployment, suspending the clip helped offload some of the weight of the membrane. A 400 g weight was suspended from the bottom of the clip to stabilize its orientation.

The deployment was displacement controlled at a rate of about 11.9 mm s−1, which was chosen to avoid significant dynamic effects while achieving a full deployment in about 4 minutes.

The average deployment forces, (FB+FB0)/2 and (F_A+F_A0)/2, measured during a single de-

ployment are plotted in Figure 2.29 with respect to the unwrapping fractionbd/Lband the unfolding fraction ad/La. As can be seen, the radial component of the deployment forces is dominant: the in-plane transverse deployment forces were about 20 times smaller than the radial force component, and the out-of-plane deployment forces were about 4 times smaller than the radial forces.

A ve rage S tage Force (N) 0 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Unwrapping force (radial) Unwrapping force (transverse) Unwrapping force (out-of-plane) Unfolding force (radial) Unfolding force (transverse) Unfolding force (out-of-plane)

Unfolding Fraction Unwrapping Fraction

Figure 2.29: Deployment force profiles. During the first stage of unwrapping, the unfolding fraction is fixed at 0, and during the second stage of unfolding, the unwrapping fraction is fixed at 1.

Figure 2.30 plots the radial component of the average deployment forces (FB +FB0)/2 and

(FA+FA0)/2 measured during three separate deployments, along with the predicted deployment

forces, computed using the models presented in Section 2.3.1.

For the unwrapping force prediction, the elastic modulus was chosen as E= 3.5 GPa, Poisson’s ratio was ν = 0.38, the coefficient of friction was µ = 0.25. The elastic properties are from the manufacturer’s specification [26].

The coefficient of kinetic friction between an aluminized Mylarr _{film (the model material) and}

a Kaptonr _{film treated with the a PTFE-based dry lubricant (the material of the cage walls) was}

measured in a separate experiment. In brief, a disc of aluminized Mylarr_{, glued to a known mass,}

was dragged over a PTFE-treated flat Kaptonr _{sample. This was done using one of the linear}

actuators described above, and the dragging forces were measured by the one of the force sensors described above. The coefficient of kinetic friction was extracted based on the force measurements and the known mass.

The unfolding force predictions use a clip length Lc = 11 mm, and a clip overlapLo = 8 mm. The clip length was measured; the clip overlap was estimated. In generating the predicted unfolding force profile, a different clip bending stiffness D was used for each snap. This is because the clip in the experiment was a paintbrush, and the number of paintbrush bristles engaged with the fold increased with each snap.

Figure 2.30 shows that both the unwrapping and the unfolding force predictions capture both the overall trends in the experimentally measured data in magnitude, and in the case of the un-

Force ( N) 0 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Experimental unwrapping forces Unwrapping model

Experimental unfolding forces Unfolding model

Unfolding Fraction Unwrapping Fraction

Figure 2.30: Experimentally measured deployment forces and model predictions.

folding stage, character. The good match between predictions and experiments suggests that the mechanisms underlying these models (that is, friction and stack bending for the unwrapping stage and clip bending for the unfolding stage) were indeed dominant during the deployment experiments. There are many physical effects not captured by these simple mechanical models. These effects include gravity, contact and sliding between the strips, the non-uniform bending stiffness of the folded stack, the snagging of the folded ligaments against each other or the cage walls, and variations in the elastic and geometric properties of the crude clips. It is expected that these unmodeled effects account for some of the discrepancies between the predicted and measured deployment forces.

Figure 2.31 shows views from an overhead camera at the beginning of deployment, at the end of the unwrapping stage, during the unfolding stage, and at the end of the deployment. Controlled deployment was observed for each of the three deployments plotted in Figure 2.30.